Answer:
Adult tickets (x) were bought for $45 while children tickets (y) at $28
Step-by-step explanation:
Complete question
(Adult tickets to Space City amusement park cost x dollars. Children's tickets cost y dollars. The Henson family bought 3 adult and 1 child tickets for $163. The Garcia family bought 2 adult and 3 child tickets for $174. a. Write equations to represent the Hensons' cost and the Garcias' cost. Hensons' cost: _, Garcias' cost: _. b. Solve the system. adult ticket price: _. Child ticket price:)
a).
Henson's family bought 3 adult tickets and 1 child ticket for $163
3x + y = 163.
Garcia's family bought 2 adult tickets and 3 children tickets for $174
2x + 3y = 174
Equations to represent their cost =
3x + y = 163 ......equation (i)
2x + 3y = 174 .......equation (ii)
b) solving the equation,
This is a simple simultaneous equation and would require any of the methods used to solve simultaneous equations either
1. Substitution method or
2. Eliminatation method.
I'll use substitution method to solve this.
3x + y = 163 .... equation (i)
2x + 3y = 174 .....equation (ii)
From equation (i)
3x + y = 163
Make y the subject of formula
y = 163 - 3x.....equation (iii)
Put y = 163 - 3x into equation (ii)
2x + 3(163 - 3x) = 174
2x + 489 - 9x = 174
Collect like terms
2x - 9x = 174 - 489
-7x = -315
x = 45.
Put x = 45 into equation (i) to solve for y
3(45) + y = 163
135 + y = 163
y = 163 - 135
y = 28.
The cost of the adult tickets is $45 while that of the children is $28
